Mathematics · the experiment
Flip the link between records and maximum
A series of daily rainfall: each record lights up, and the last one is the maximum. First count records with no dry days, then add dry days and find the share that flips the shape of the link.
1 · Count records with no dry days
Beginner
In a series with no dry days, what does the number of records tell you about how high the maximum is?
It rains every day. Lengthen the series to the shortest one that holds 4 records on average.
2 · Find the dry-day threshold
Intermediate
Group A: about half the days dry, with a predicted threshold of 0.315. What shape did the link take as the series got longer?
Dry days join in, with a share q. The curve follows the link between records and maximum as the series gets longer. Set q at the switch, where the curve stops falling right from the start.
3 · Change the rainfall distribution
Expert
With q = 0.42, how does the link start for uniform rain, and for exponential rain?
Rain on wet days now follows a uniform distribution. Find again the share of dry days that flips the shape of the link.
4 · Make the series endless
Expert
Over very long series, the link dies out as a power of their length. What sets the exponent?
Link flipped
—